Exciton polariton condensation from bound states in the continuum at room temperature

Exciton–polaritons (polaritons) resulting from the strong exciton–photon interaction stimulates the development of novel low-threshold coherent light sources to circumvent the ever-increasing energy demands of optical communications1–3. Polaritons from bound states in the continuum (BICs) are promising for Bose–Einstein condensation owing to their theoretically infinite quality factors, which provide prolonged lifetimes and benefit the polariton accumulations4–7. However, BIC polariton condensation remains limited to cryogenic temperatures ascribed to the small exciton binding energies of conventional material platforms. Herein, we demonstrated room-temperature BIC polariton condensation in perovskite photonic crystal lattices. BIC polariton condensation was demonstrated at the vicinity of the saddle point of polariton dispersion that generates directional vortex beam emission with long-range coherence. We also explore the peculiar switching effect among the miniaturized BIC polariton modes through effective polariton−polariton scattering. Our work paves the way for the practical implementation of BIC polariton condensates for integrated photonic and topological circuits.


Table of Content
We made numerical simulations of PhC lattice mode dispersion (the simulation details are depicted in Note S2, similarly hereinafter) for samples with thickness l of 120 and 160 nm while keeping other parameters as constants (period a = 292 nm, and radius of etched hole r = 57 nm).The result of l = 140 nm is depicted as an example of simulation in Note S2 and hence is not shown here.
The simulations in Figs.S20a-b imply that BIC polariton modes LP1, and LP3 redshift as the sample thickness increases, which is consistent with experimental results in Fig. S19.We note that the Q factor of LP3 increases greatly at a small angle when l = 140 nm, while this trend is much weakened when l = 160 nm and not applicable when l = 120 nm.Considering the actual range of thickness of CsPbBr3 microplatelets, the samples with thickness l ~145 ± 5 nm are ideal for FIB etching.Regarding the etching depth, we observed that it has a notable impact on the mode dispersion of the BIC polaritons (Fig. S21).Compared with the fully etched sample with similar parameters, the partially etched sample exhibits single parabolic dispersion and is blurred at large angles.We considered that the partial etching would influence its mirror image in the Z-axis direction.The inversion symmetry and mirror-flip symmetry are all broken causing the degradation of the theoretical infinite-lifetime BIC state and is replaced by a leaky resonance 7 .Although under high-power excitation, we could still observe the lasing character at zero momentum, the emission cannot be ascribed to the condensation of the BIC state now, but related to the leakage mode at TE polarization.separated topological charges at off Γ points.Since the structure still preserves mirror symmetry, the split BICs are constrained in the TM direction 8 .In the angle-resolved PL spectra, two laser-like emissions appear at symmetric angles around the zero momentum, which coincide with the two symmetric subbranches in the angle-resolved reflectance spectra (Figs.S22b-c).The BIC characteristics at off Γ points need further investigation and will not be discussed here.The corresponding numerical simulations of etching depth and distortion are provided in Fig. S23.In Fig. S23a, the structure comprises cylindrical holes that are incompletely etched through the microplatelet.resulting in a limited hole depth of 70 nm.Conversely, Fig. S23b showcases elliptical holes with a semi-minor axis of 28.5 nm and a semi-major axis of 57 nm.All other parameters remain consistent with the simulation example described in Note S2.Notably, neither of these structures exhibits a BIC state at zero momentum, despite the dominance of parabolic modes, which aligns with the experimental results.Due to the challenges associated with altering the sidewalls of the etched holes while keeping other parameters unchanged, our analysis primarily focuses on investigating the influence of oblique sidewalls using numerical simulations.Specifically, we employ a bowl-shaped configuration with etched holes characterized by an upper radius of 57 nm and a lower radius of 30 nm.The simulation results presented in Fig. S24a suggest that the incline of the sidewall does not affect the location of the BIC state at Γ point of the first Brillouin zone.Despite the absence of mirror-flip symmetry in this structure, the inversion symmetry remains intact.
We compare the Q factors of oblique sidewalls with those of vertical sidewalls (as exemplified in the simulation example described in Note S2), as shown in Fig. S24b.The results reveal a significant increase in the Q factor of LP3 when structures are formed at a small angle in both cases.
Nevertheless, this increase is somewhat attenuated in the structure featuring oblique sidewalls, indicating a potential decrease in the Q factor.We observed rough surface features near the etched holes in the SEM images depicted in Fig. S3, ascribing to ion beam etching.These residues introduced by the etching process can increase coupling with nearby radiative states by scattering, posing a drawback to the Q factors of BICs.To mitigate such disadvantages during the etching process, it is crucial to confine the residues exclusively to the boundary of the etched hole, while ensuring they do not persist on the unetched surface or obstruct the hole.To address this concern, we employed the FEI Nova 200 NanoLab FIB system and positioned the sample stage at an inclination angle of 52°.This arrangement ensured that the ion beam source was incident vertically on the sample, resulting in sharper sidewalls and fewer residues.
Concurrently, the electron beam source was obliquely incident on the sample, allowing continuous observation of the etching state throughout the process.By adopting this approach, we minimized the influence of residues as much as possible.
To address any potential concerns regarding Galium ion contamination resulting from the etching process, we performed energy dispersive spectroscopy (EDS) elemental analysis of the etched sample, as shown in Fig. S25 and Table S1.The obtained results reveal a minimal presence of gallium ions.Notably, in the etching process, we deliberately utilized a very low ion beam current (<10 pA), and ensured a short residence time (maximum of 2 ms), effectively mitigating any substantial gallium ion contamination in the sample.

LU
Ck and , () = and indicates the photonic or excitonic weight.For the LPB, they are given by: 30/35

Note S3. Polariton dispersion and BIC states at different detuning
The detuning of cavity mode relative to the excitonic resonance can be precisely controlled by the lattice period a.We define the detuning as the offset of dark Mode 3 relatives to excitonic resonance (Ex = 2.41 eV).Fig. S27a     Furthermore, the BIC polariton lifetime can be expressed as the inverse to the population decay rate, that is 14 , γLP = |X|  ps.It should be noted that the quality factor obtained from the angle-resolved reflectance spectra may underestimate the exact cavity quality factor.On the other hand, for CsPbBr3 perovskites excited by femtosecond pulsed laser at room temperature, the excitonic non-radiative recombination processes may involve polaron-assisted energy transfer, Auger recombination, and exciton-exciton annihilation, etc.Hence, in our case, we should not ignore the cavity photon out-coupling part considering the limited cavity quality factor in practice.Then, considering a |X| 2 of ~0.20 and an excitonic nonradiative lifetime of ~60 ps, a polariton lifetime of ~3.1 ps could be estimated, which agrees with our experimental results.The far-field emission of the CsPbBr3 PhC lattice was simulated by the 3D FDTD method.The geometrical parameter was set as periodicity a = 292 nm, radius of etched hole r = 57 nm, thickness h = 140 nm.Due to the limitation of computing performance, the simulated region was limited as an area consisting of 40 × 40 unit cells, and the mesh grid was set as 5 nm × 5 nm × 10 nm.Two incoherent electrical dipoles with s and p polarization were arranged at the center of the simulating object 15 .The near-field monitor was set slightly above the PhC surface to record the electromagnetic field.Far-field distribution was obtained by the built-in far-filed projector.Since the PL emission of CsPbBr3 PhC covers the wavelength mainly from 515 to 540 nm, we take the far-field projection containing multiple wavelengths into the final simulation.Each of the far-field projections can be viewed as a slice of the electromagnetic field at a constant wavelength 16 .Some of these far-field projections of electric field || 2 are shown in Fig. S30.Then we sum all the slices together, as is shown in Fig. 4c of the main text.The simulated result is mainly satisfied with the experiment in Fig. 4a of the main text, including the elliptical-shaped photonic bands along kx and ky directions, and the dark region around these bands.The BIC polariton condensate emission pattern in Fig. 4b of the main text exhibits the donut shape with a much smaller size than the overlapped region of elliptical-shaped photonic bands along kx and ky directions.This can be partly explained by the simulated far-field projection at 526 nm in Fig. S30.At this wavelength, a circular electromagnetic field pattern is observed at the vicinity of the Γ-point, which is qualitatively smaller than the overlapped region of elliptical-shaped photonic with high energy and large momentum (e.g., far-field projection at 522 nm and 524 nm).However, the BIC polariton condensates around the Γ-point dominate the emission pattern, i.e., emissions of the same wavelength at other momentum coordinates are suppressed, which is not reproduced in this simulation.

Fig. S3 .
Fig. S3.Schematic of the fabrication and SEM images of the CsPbBr3 PhC lattice.

Fig. S7 .
Fig. S7.Real-space images of the laser spot and the CsPbBr3 PhC lattice emission.

Fig. S8 .
Fig. S8.Evolution of emission spectra with different pump densities of CsPbBr3 PhC lattices at different detunings in the vicinity of Pth.

Fig. S11 .
Fig. S11.Mode splitting resulting from the optical birefringence of the orthorhombic CsPbBr3 single crystals.

Fig. S14 .
Fig. S14.Interference patterns of another sample in real space.

Fig. S16 .
Fig. S16.Interference patterns in momentum space with the two arms misaligned.

Fig. S18 .
Fig. S18.Switching performance of different signal and gating conditions.Note S1.Influence of the FIB etching process on the morphology and performance.Fig. S19.Influence of thickness of CsPbBr3 microplatelets.

Fig. S23 .
Fig. S23.Simulation of angle-resolved reflectance spectra of the PhC structure with partial etching and distortion.

Fig. S24 .
Fig. S24.Simulation of angle-resolved reflectance spectra of the PhC structure with oblique sidewall.Fig.S25.EDS elemental analysis spectrum.Table S1.Elemental analysis of the etched region of CsPbBr3 microplatelets.Note S2.Numerical simulation of PhC lattice mode dispersion.Fig. S26.Simulated mode dispersion of CsPbBr3 PhC lattice.Note S3.Polariton dispersion and BIC states at different detunings.Fig. S27.Experimental and simulated angle-resolved reflectance spectra of CsPbBr3 PhC lattices with different detunings.

Fig. S28 .
Fig. S28.Angle-resolved PL spectra of CsPbBr3 PhC lattices with different detunings.Note S4.Time-resolved spectrum of BIC polariton condensation Fig. S29.Time-resolved PL of the BIC polariton condensate.Note S5.Numerical simulation of Fourier space distribution of PhC modes Fig. S30.Simulated far-field distribution of electric field intensity at different wavelengths.

Fig. S1 |Fig. S2 |
Fig. S1 | Morphologic characterizations of single-crystalline CsPbBr 3 microplatelets.a-b, Optical and scanning electron microscope (SEM) images of CsPbBr3 microplatelets on Si/SiO2 substrates, both the uniform color and smooth surface indicate a high crystal quality.c, The surface roughness and sample thickness were estimated to be around 1.9 nm and 146 nm in a scan area of 10 × 10 μm 2 by atomic force microscopy.d, X-ray diffraction patterns of the CsPbBr3 microplatelets.The sharp peaks at 14.9°, 15.1°, 30.3°, and 30.6° correspond to (002), (110), (004), and (220) planes of orthorhombic phase, respectively, matching well with the standard structure reported in ref1  .

Fig. S3 |Fig. S4 |
Fig. S3 | Schematic of the fabrication and SEM images of the CsPbBr 3 PhC lattice.a, Schematic diagram illustrating the growth, transfer, and focused ion beam (FIB) milling processes of singlecrystalline CsPbBr3 microplatelets.Out-of-plane CsPbBr3 microplatelets were fabricated by the chemical vapor deposition method on silicon substrates.Subsequently, they were transferred onto the target substrate.FIB with optimized etching paths was applied to achieve precise carving of the airhole array on the microplatelet.b, SEM image of the etched air holes on the CsPbBr3 microplatelet, arranged in a square lattice.c, Zoomed-in image of (b).d, Tilt-view SEM image of the CsPbBr3 PhC lattice The sharp sidewalls and smooth surface indicate negligible damage caused by FIB milling.Scale bars for (b)-(d) are 1.2 μm, 250 nm, and 250 nm, respectively.

Fig. S5 |
Fig. S5 | Simulated angle-resolved reflectance spectra of CsPbBr 3 PhC lattices with different number of periods (N).a-d, Simulated angle-resolved reflectance spectra of CsPbBr3 PhC lattice with N values of 5, 10, 20, and 40, respectively.e, Simulated angle-resolved reflectance spectra of CsPbBr3 PhC lattice with an infinite number of periods.

Fig. S6 |
Fig. S6 | Extraction of polariton modes of CsPbBr 3 PhC lattice.a, Angle-resolved reflectance spectrum of the CsPbBr3 PhC lattice taken from Fig. 1e of the main text.b, The corresponding numerical simulation of (a).The simulation data is reproduced from Fig. S24c in Note S2.The blue dotted regions are indicated as the LP3 polariton modes for extraction.c, The extracted energies and Q factors of the LP3 polariton mode near 0° in (a).d, The extracted energies and Q factors of the LP3 polariton mode near 0° in (b).The highest Q factor of 913 is observed in the vicinity of the

Fig. S7 |Fig. S8 |
Fig. S7 | Real-space images of the laser spot and the CsPbBr 3 PhC lattice emission.a, From left to right: the optical images depict the laser spot, the CsPbBr3 PhC lattices without laser pumping, and the CsPbBr3 PhC lattices with partial laser pumping.The CsPbBr3 PhC lattices exhibit higher emission intensity than the pristine microplatelet, indicating the enhancement effect achieved in the PhC lattice.b, The real-space PL images of the CsPbBr3 PhC lattice under pulsed laser excitation with the pump density below and above Pth, respectively.

Fig. S9 |
Fig. S9 | Pump density-dependent emission spectra of CsPbBr 3 PhC lattices at different detunings.a, Δ= −64.1 meV.b, Δ= −74.6 meV.To enhance visual clarity, the pseudocolor scale has been adjusted to accommodate two distinct ranges of pump density.The yellow dashed lines indicate the polariton condensation threshold.

Fig. S10 |Fig. S11 |
Fig. S10 | Simulated excitonic weight of CsPbBr 3 PhC lattices with different detunings.Polariton energy-angle dispersion calculated from the coupled harmonic oscillator model of CsPbBr3 PhC lattices with Δ = −64.1 meV (a) and −74.6 meV (b), respectively.The colors in the images represent a linear representation of the excitonic fraction for each mode, ranging from 0 (photon) to 1 (exciton).

Fig
Fig. S12 | Quasi-continuous-wave optically pumped BIC polariton condensation at cryogenic temperatures.a-c, The 2D pseud-color mapping for PL spectra as the pump density increases for two CsPbBr3 PhC lattices, sample 1 at 80 K (a), as well as sample 2 at 80 K (b) and 90 K (c).Notably, BIC polariton condensation could not be observed in sample 1 above 80 K and sample 2 above 90 K, indicating the potential for further improvement in sample quality.A clear transition from spontaneous emission to a condensate state was observed.The polariton condensation threshold of sample 2 at 90 K slightly increased compared to that at 80 K. d-e, The 2D pseud-color mapping for PL spectra as the pump density increases for two pristine CsPbBr3 microplatelets.

Fig. S13 |
Fig. S13 | Spatial coherence of the CsPbBr 3 PhC lattice.a-b, Superposition of the real-space image and its inverted image for the CsPbBr3 PhC lattice below and above Pth.In the absence of polariton condensation (a), the system exhibits a sharp coherence line with a correlation length below 1 μm, indicating that it remains in the thermal regime.When pumped above Pth (b), clear interference fringes emerge in the superposition region, suggesting a long-range spatial coherence.c-d, A spatial coherence distribution was derived from a cross-section of the interference pattern in (b).Through fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) processes, the pure interference signal (red line) was isolated from the baseline (blue line).The amplitude profile of the spatial coherence was then determined based on the envelopes of the interference signal.A spatial coherence length of 8.7 μm was obtained with a Gaussian function fitting.

Fig. S15 |
Fig. S15 | Interference patterns of BIC polariton condensate emission in momentum space.a, Schematic of the Michelson interferometer integrated into the Fourier system.The superposition of the original image and its inverted counterpart results in a mirror-symmetrical interference image.bc, Back-focal plane (BFP) images of BIC polariton condensate emission collected from the left (b) and right arm (c) of the interferometer.d, Michelson interference pattern obtained by overlapping (b) and (c).e, Magnified interference pattern from (d), where two forks exhibiting a mirror-symmetric configuration are observed.

Fig. S16 |
Fig. S16 | Interference patterns in momentum space with the two arms misaligned.BFP images of BIC polariton condensate emission collected from the left arm (first column), the right arm of the interferometer (second column), and their interference pattern (third column), with distinct misaligned distances (0 < Δx1 < Δx2 < Δx3).

Fig. S17 |Fig. S18 | 2 Energy# 1 .
Fig. S17 | Real-space emission images of the miniaturized BIC polaritonic modes.a, Optical image of the measured CsPbBr3 PhC lattice.Scale bar: 10 μm.b-d, Real-space PL image of the CsPbBr3 PhC lattice under the excitation of the signal beam (~Pth, b), the gate beam (~0.2 Pth, c), and two beams together (d).e-f, Real-space PL image of the emission from the miniaturized BIC polaritonic modes M11 (e) and M12 (f).

Fig. S19 |
Fig. S19 | Influence of thickness of CsPbBr 3 microplatelets.a, SEM images of the CsPbBr3 PhC lattice with different sample thicknesses for etching.Scale bar: 1 μm.b, Corresponding angleresolved reflectance spectra respectively to (a).c, Angle-resolved PL spectra with the pump density below (left panel) and above Pth (right panel), respectively.

Fig. S20 |# 2 .
Fig. S20 | Simulation of angle-resolved reflectance spectra with different sample thicknesses.a, l = 120 nm.b, l = 160 nm.Inserts are corresponding sketch maps of the side view (upper) and top view (lower) of CsPbBr3 PhC lattices.c, The extracted Q factors of bright polariton modes LP2 and corresponding dark modes LP3 for samples with different l.

Fig. S21 | 4 zC
Fig. S21 | Influence of the depth of etching.a, SEM images of the CsPbBr3 PhC lattice with excessive (upper) and insufficient (lower) etching depths.Scale bar: 1 μm.b, The corresponding angle-resolved reflectance spectra.c, Corresponding angle-resolved PL spectra with the pump density below (left panel) and above Pth (right panel).

Fig. S22 |
Fig. S22 | Influence of the distortion during etching.a-b, SEM images of the CsPbBr3 PhC lattice with different distortion statuses during etching.Scale bar: 1 μm.c-d, Angle-resolved reflectance spectra corresponding to (a) and (b).e-f, Angle-resolved PL spectra with the pump density below (left panel) and above Pth (right panel) corresponding to (a) and (b).

Fig. S23 |
Fig. S23 | Simulation of angle-resolved reflectance spectra of the PhC structure with partial etching and distortion.a, Etched holes with a depth of 70 nm.b, Elliptical holes with their semiminor axis of 28.5 nm and semi-major axis of 57 nm.Inserts are corresponding sketch maps of the side view (upper) and top view (lower) of CsPbBr3 PhC lattices.

# 3 .
Influence of oblique sidewall during the etching process.

Fig. S24 |# 4 .
Fig. S24 | Simulation of angle-resolved reflectance spectra of the PhC structure with oblique sidewall.a, Bowl-shaped etched holes with an upper radius of 57 nm and a lower radius of 30 nm.Inserts are corresponding sketch maps of the side view (upper) and top view (lower) of CsPbBr3 PhC lattices.b, The extracted Q factors of bright polariton modes LP2 and corresponding dark modes LP3 at different morphologies of the sidewall.

Fig. S25 |
Fig. S25 | EDS elemental analysis spectrum.a, Psedu-color EDS images of Cs, Pb, Br, and Ga elements in uniformly distributed CsPbBr3 microplatelet, respectively.The regions of white dotted lines represent etched areas.b, The corresponding SEM image.Scale bar: 5 μm.c, The content of each element in the entire scanning area.
energy.The dispersion and linewidth of Mb and Md are imported from simulated PhC mode dispersion as discussed in Fig. S25.Exciton energy and linewidth are set as 2.14 eV and 60 meV based on fitting of excitonic absorption in Fig. S2.In this way, the anti-crossing of both bright and dark modes can be interpreted.The eigenvectors of UPs/LPs are expressed as: ,, , shows the angle-resolved reflectance spectra of CsPbBr3 PhCs with different lattice periods.From left to right, a = 290, 295, 300, and 300 nm, respectively.The thickness of the left three samples is l = 140 nm while the sample on the right side is l = 150 nm.The yellow and red solid lines are polariton branches fitted by the coupled harmonic oscillator model.The corresponding cavity Mode 2 and Mode 3 can thus be deduced.The detuning becomes more negative as the period increases.Although the thickness of the sample can also result in different detuning, it is difficult to arbitrarily adjust due to technical limitations.Fig. S27b is the corresponding numerical simulation results of polariton dispersion by FDTD methods.

Fig. S27 |
Fig. S27 | Experimental and simulated angle-resolved reflectance spectra of CsPbBr 3 PhC lattices with different detunings.a, Experimental angle-resolved reflectance spectra of CsPbBr3 PhC lattice with Δ of −52.5, −64.1, −119.1, and −158.8 meV, respectively.The solid lines are fitted polariton branches and black dashed lines are the corresponding photonic modes.b, The corresponding simulated results.

Fig. S28 presents
Fig.S28presents the corresponding angle-resolved PL spectra below and above Pth.From left to right, Mode 3 exhibits an increasingly negative detuning, leading to a redshift of the LP3.However, when the detuning is too negative, polariton condensates at this BIC energy become unfavorable due to the amplified loss before reaching the final condensation.Consequently, lasing actions may occur at alternative polariton branches or even other BIC modes with higher energy, such as LP1 at Δ = −158.8meV.

Fig. S28 |
Fig. S28 | Angle-resolved PL spectra of CsPbBr 3 PhC lattices with different detunings.a, Under pulsed laser excitation with a pump density below Pth.b, Under pulsed laser excitation with a pump density above Pth.The marked LP1 and LP3 indicate the position of the BIC state at these modes.

Fig. S29 |
Fig. S29 | Time-resolved PL of BIC polariton condensates.a, Angle-resolved PL spectra of the measured CsPbBr3 PhC lattice with different detunings.From left (No. 1) to right (No. 3), the energy of BIC polariton mode increases due to weaker negative detuning.b, The corresponding polariton condensation of these BIC polariton modes, which is ready for time-resolved PL measurements.c, Time-resolved PL emission of BIC polariton condensates at pump densities of 1.1 Pth (No. 1-3) and 1.6 Pth (No. 3), respectively.Continuous red-shift can be observed in these measurements.d, The normalized time-resolved intensity profiles at 1.1 Pth extracted from (c).The decay region can be fitted by the mono-exponential decay function.e, The normalized time-resolved intensity profiles of No. 3 at 1.6 Pth.As the pump density increases from 1.1 Pth to 1.6 Pth, The intensity profiles can be fitted by a mono-exponential or biexponential decay function.

Fig. S30 |
Fig. S30 | Simulated far-field distribution of electric field intensity at different wavelengths.
[4][5][6]The fitted excitonic absorption (blue 81 dotted line) suggests the narrow full width at half maximum (FWHM) of approximately 59.5 meV.Normalized photoluminescence (PL) spectra of the CsPbBr3 microplate and photonic crystal (PhC) 82 b, 83 lattices obtained by pumping with a continuous-wave laser.PL emission from the CsPbBr3 84 microplatelet exhibits an emission peak of 2.39 eV.The PL spectrum of the PhC lattice exhibits an 85 energy redshift and a combination of multiple peaks, indicating the presence of coupling between the 86 excitonic emission and PhC lattice cavity modes.c, Time-resolved PL spectra of CsPbBr3 87 microplatelets and PhC lattices.The PL from CsPbBr3 microplatelets shows a single-exponential 88 decay with a lifetime of approximately 6.0 ns, which serves as evidence of its high quality and low 89 trap density.In contrast, the PL from CsPbBr3 PhC lattices displays a fast decay rate, which may be 90 attributed to the modulation of the Purcell effect.

Table S1 | Elemental analysis of the etched region of CsPbBr 3 microplatelets.
2